Analysis of the Chickenpox Disease Evolution in an MSEIR Model Using Fractal-Fractional Differential Operator

The main aim to conduct this research study is to show the advantage of using fractal-fractional differential operator over other differential operators in epidemiology. In this regard, an MSEIR mathematical model with fractal-fractional differential operator is being taken to study the qualitative analysis of the evolution of the chickenpox disease spread among the children of schools based in Schenzhen city of China in 2013. Balancing the dimensions of every differential equation by carrying the appropriate power on each dimensional quantity we prove the existence and uniqueness of the solutions of the said model using Schaefer’s theorem and fixed-point theory. Further, Ulam–Hyers stability of the model is shown. Comparing the results of our model with those of previously existed models with integer-order and other fractional-order derivatives, we show, using the real data of 25 weeks, that results of our model have come out with significant amount of accuracy, i.e., the fractal-fractional differential operator follows the disease evolution process more accurately than other operators. Numerical simulations are carried out using an efficient numerical technique and a MATLAB routine called ’fmincon’ is used to optimize the values of fractal and fractional orders as well as the transmission rate.